Problem: Multiply the following complex numbers, marked as blue dots on the graph: $(2) \cdot (3 e^{19\pi i / 12})$ (Your current answer will be plotted in orange.)
Explanation: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $2$ ) has angle $0$ and radius $2$ The second number ( $3 e^{19\pi i / 12}$ ) has angle $\frac{19}{12}\pi$ and radius $3$ The radius of the result will be $2 \cdot 3$ , which is $6$ The angle of the result is $0 + \frac{19}{12}\pi = \frac{19}{12}\pi$ The radius of the result is $6$ and the angle of the result is $\frac{19}{12}\pi$.